A145867 Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.

1, 2, 6, 20, 74, 292, 1214, 5252, 23468, 107672, 505048, 2413776, 11723188, 57737032, 287853518, 1450697572, 7381645844, 37884748712, 195947389208, 1020610698832, 5349968198328, 28208066576176, 149526042974008, 796520870628752, 4262367319460848

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = sum(j,0,n, C(n,j)*A001006(j)*A001006(n-j)), where C(n,j) = n!/(j!(n-j)!).

Recurrence: (n+2)*(n+4)*a(n) = 6*(n^2 + 3*n + 1)*a(n-1) + 4*(n-1)*(n+1)*a(n-2) - 24*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ 9 * 6^(n+1) / (Pi * n^3). - Vaclav Kotesovec, Feb 18 2015

E.g.f.: exp(2*x)*BesselI(1,2*x)^2/x^2. - Ilya Gutkovskiy, Sep 21 2017

Mathematica

Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Array[Mot, 21, 0]; For[i = 0, i < 21, ++i, Mot[i] = Sum[Binomial[i, 2*j]*Cat[j], {j, 0, Floor[i/2]}]]; Table[Sum[Binomial[n, j]*Mot[j]*Mot[n - j], {j, 0, n}], {n, 0, 15}]

Crossrefs

Cf. A001006.

Sequence in context: A150156 A150157 A371712 * A188144 A245734 A150158

Adjacent sequences: A145864 A145865 A145866 * A145868 A145869 A145870

Keyword

nonn

Author

Eric S. Egge, Oct 22 2008

Extensions

More terms from Alois P. Heinz, Feb 18 2015

Status

approved